Hereditary Memory Research Articles

Dynamics of stochastic FitzHugh–Nagumo system on unbounded domains with memory

In this paper, we consider the non-autonomous stochastic FitzHugh–Nagumo system with hereditary memory and a very large class of nonlinearities, which has no restriction on the upper growth of the nonlinearity. The existence of a random pullback attractor is established for this system in all N-dimensional space.

Unified neuroadaptive fault-tolerant control of fractional-order systems with or without state constraints

The problem of controlling fractional-order nonlinear systems remains interesting and challenging due to the powerful and hereditary memory features of such systems. In this paper, we investigate the adaptive tracking control problem for a class of fractional-order nonlinear systems with or without state constraints. The tan-type barrier Lyapunov function (BLF) is adopted for the first time in fractional Lyapunov direct method. Such technique allows for the accommodation of the situations with and without state constraints in a unified framework. Moreover, neural network (NN) is utilized to reconstruct the sophisticated nonlinear functions arising from the fractional-order differentiation of the virtual controller, resulting in a neuroadaptive fault-tolerant control scheme. It is shown that, with the proposed unified control, all the closed-loop signals are semiglobally ultimately uniformly bounded whether state constraints are imposed or not. Both theoretical analysis and numerical simulation confirm the effectiveness of the developed approach.

Asymptotic Behaviour of the Eenergy to the Viscoelastic Wave Equation with Localized Hereditary Memory and Supercritical Source Term

Asymptotic Behaviour of the Eenergy to the Viscoelastic Wave Equation with Localized Hereditary Memory and Supercritical Source Term

Efficient Exponential Time-Differencing Methods for the Optical Soliton Solutions to the Space-Time Fractional Coupled Nonlinear Schrödinger Equation

The coupled nonlinear Schrödinger equation is used in simulating the propagation of the optical soliton in a birefringent fiber. Hereditary properties and memory of various materials can be depicted more precisely using the temporal fractional derivatives, and the anomalous dispersion or diffusion effects are better described by the spatial fractional derivatives. In this paper, one-step and two-step exponential time-differencing methods are proposed as time integrators to solve the space-time fractional coupled nonlinear Schrödinger equation numerically to obtain the optical soliton solutions. During this procedure, we take advantage of the global Padé approximation to evaluate the Mittag-Leffler function more efficiently. The approximation error of the Padé approximation is analyzed. A centered difference method is used for the discretization of the space-fractional derivative. Extensive numerical examples are provided to demonstrate the efficiency and effectiveness of the modified exponential time-differencing methods.

Fundamentals of Economic Genetics in Models of Evolution and Revitalization of Old Industrial Regions

The review article is devoted to a search for unconventional solutions to established problems of old industrial regions. The economy of historically industrial territories is under the influence of long-term and complex factors of industrial specialization, socio-demographic processes, cultural and moral norms of the population, as well as political fronts. These factors are involved in modeling the system of "hereditary memory" of regions, which is responsible for regional predisposition to a certain type of innovative, social, industrial, political and other processes. The aim of the study is to identify genetic codes that determine the specific features of socio-economic transformations in old industrial regions. The hypothesis of the research is that the socio-economic development of an old industrial region is to a certain extent determined by a system of its interrelated genetic codes that determine the established specialization and predisposition of the territory to various endogenous processes. The methodology of the survey study is made up of the methods of system-functional and system-historical analysis of scientific publications, reflecting solutions to the problems of socio-economic development of old industrial regions. It is substantiated that each old industrial region has “defining” genetic codes: production, social and institutional ones. Together, these codes represent the fundamental hereditary program of the economic evolution of the territory and contain a set of endogenous factors of the development of the territory, formed and transmitted from generation to generation in the process of the life of society. It is shown that each region also has “dynamic” genetic codes that can be identified as innovative, infrastructural and sociocultural. All these codes are generated at the level of the connections of "defining" codes; they are able to cause revitalization of territories and ensure further stages of the evolutionary development of the territories under consideration, provided that these compounds are not defective. The scientific novelty of the results lies in the development of theoretical and methodological provisions of economic genetics as a modern interdisciplinary science, allowing one to understand in a new way the determinants and patterns of development of industrial regions, based on the experience of old industrial territories. The practical significance of the results obtained lies in the possibility of their use by the authorities as an additional tool for the development of tactical and strategic solutions to stable problems of historically industrial territories, increasing the effectiveness of their implementation.

Climbing up the memory staircase: Equatorial zoom-whirl orbits

The nonlinear, or null gravitational memory effect for zoom-whirl orbits around fast spinning Kerr black holes for extreme mass ratio systems has a staircase structure. The latter is characterized by a periodic fast increase in the memory during the whirl phases of the orbit, and near constant levels when the orbit is near apoapsis. We study the contribution of different spherical harmonic modes to this effect, and discuss the relative importance thereof. Because the hereditary memory effect increases in magnitude linearly in the number of periapsis passages on a dynamical time scale, while the oscillatory parent gravitational waves are sourced by an orbit that evolves on a much longer radiation reaction time scale, the magnitude of the former relative to the latter increases with time. We also consider orphan memory and the memory effect for extreme mass ratio inspirals. We then discuss the prospect of detection with the Laser Interferometer Space Antenna (LISA).

Uniform Attractors of Nonclassical Diffusion Equations Lacking Instantaneous Damping on $\mathbb{R}^{N}$ with Memory

In this paper, we consider the non-autonomous nonclassical diffusion equations on $\mathbb{R}^{N}$ with hereditary memory $$ u_{t} -\Delta u_{t} - \int _{0}^{\infty }\kappa (s) \Delta u(t-s)ds+ f(x,u) = g (x,t). $$ The main characteristics of the model is that the equation does not contain a term of the form $-\Delta u$ , which contributes to an instantaneous damping. We first investigate the existence and uniqueness of weak solutions to the initial-boundary-value problem for above-mentioned equation. Next, we study the long-time dynamical behavior of the solutions in the weak topological space $H^{1}(\mathbb{R}^{N}) \times L^{2}_{\mu }(\mathbb{R}^{+},H^{1}( \mathbb{R}^{N}))$ , where the nonlinearity is critical and the time-dependent forcing term is only translation bounded instead of translation compact. The results in this paper will extend and improve some results in (Conti et al. in Commun. Pure Appl. Anal. 19:2035–2050, 2020) in the non-autonomous and unbouded domain cases which have not been studied before.

Nonclassical diffusion with memory lacking instantaneous damping

We consider the nonclassical diffusion equation with hereditary memory \begin{document}$ u_t-\Delta u_t -\int_0^\infty \kappa(s)\Delta u(t-s)\,{{\rm{d}}} s +f(u) = g $\end{document} on a bounded three-dimensional domain. The main feature of the model is that the equation does not contain a term of the form $ -\Delta u $, contributing as an instantaneous damping. Setting the problem in the past history framework, we prove that the related solution semigroup possesses a global attractor of optimal regularity.

Epigene Networks: Theory, Models, and Experiment

The article describes a concept of epigene networks that attempts to clarify the phenomenon of heredity and presents the results of long-term studies of the control gene and epigene networks in which the authors used an integrative approach with the tools of mathematical biology, cybernetics, genetic engineering, and bioinformatics. Epigene networks are control gene networks with epigenetic properties or those containing epigenes. By epigene, we mean special hereditary units with at least two modes of functioning of the genes subordinate to them that are capable of maintaining each of the modes in a successive series of generations. Epigenes are the units of functional hereditary memory; they perform a special role in ontogeny and phylogeny. Epigenetic systems can be designed and synthesized experimentally. One such systems is a two-component, stationary epigene with specified and controlled inherited dynamic properties that functions in vivo. Artificial epigenetic constructions can serve as models of the mechanisms of differentiation and cellular memory and can be used as bacterial biosensors. The generalized threshold models of natural and synthetic molecular genetic systems for the control of gene expression have both analytical and predictive value.

Global existence and stability of a class of nonlinear evolution equations with hereditary memory and variable density

In this paper, we consider the initial boundary value problem of nonlinear evolution equation with hereditary memory, variable density, and external force term \t\t\t{|ut|ρutt−αΔu−Δutt+∫−∞tμ(t−s)Δu(s)ds−γΔut=f(u),(x,t)∈Ω×R+,u(x,t)=0,(x,t)∈∂Ω×R+,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document} $$\\begin{aligned} \\textstyle\\begin{cases} \\vert u_{t} \\vert ^{\\rho }u_{tt}-\\alpha \\Delta u-\\Delta u_{tt}+\\int_{-\\infty } ^{t}\\mu (t-s)\\Delta u(s)\\,ds-\\gamma \\Delta u_{t}=f(u), \\\\ \\quad (x,t)\\in \\varOmega \\times \\mathbb{R}^{+},\\\\ u(x,t)=0,\\quad (x,t)\\in \\partial \\varOmega \\times \\mathbb{R}^{+},\\\\ u(x,0)=u_{0}(x),\\qquad u_{t}(x,0)=u_{1}(x),\\quad x\\in \\varOmega. \\end{cases}\\displaystyle \\end{aligned}$$ \\end{document} Under suitable assumptions, we prove the existence of a global solution by means of the Galerkin method, establish the exponential stability result by using only one simple auxiliary functional, and give the polynomial stability result.

Exponential Stability for a Transmission Problem of a Viscoelastic Wave Equation

This paper is concerned with the study of a transmission problem of viscoelastic waves with hereditary memory, establishing the existence, uniqueness and exponential stability for the solutions of this problem. The proof of the stabilization result combines energy estimates and results due to Gerard (Commun Partial Differ Equ 16:1761–1794 (1991)) on microlocal defect measures.

A singular cahn-hilliard-oono phase-field system with hereditary memory

We consider a phase-field system modeling phase transition phenomena, where the Cahn-Hilliard-Oono equation for the order parameter is coupled with the Coleman-Gurtin heat law for the temperature. The former suitably describes both local and nonlocal (long-ranged) interactions in the material undergoing phase-separation, while the latter takes into account thermal memory effects. We study the well-posedness and longtime behavior of the corresponding dynamical system in the history space setting, for a class of physically relevant and singular potentials. Besides, we investigate the regularization properties of the solutions and, for sufficiently smooth data, we establish the strict separation property from the pure phases.

Global attractors for nonclassical diffusion equations with hereditary memory and a new class of nonlinearities

We study the existence and long-time behavior in terms of existence of global attractors of weak solutions to a class of nonclassical diffusion equations with hereditary memory and a new class of nonlinearities, which contains all nonlinearities of polyno

Semiotics of a Superorganism

Darwinian evolution, as it was first conceived, has two dimensions: adaptation, that is, selection based upon “apt function”, defined as the “good fit” between an organism’s metabolic and biological demands and the environment in which it is embedded; and heredity, the transmissible memory of past apt function. Modern Darwinism has come to focus almost exclusively on hereditary memory, eclipsing the—arguably still-problematic—phenomenon of adaptation. As a result, modern Darwinism retains, at its core, certain incoherencies that, as long as they remain unresolved, preclude the emergence of a fully-coherent theory of evolution. Resolving the incoherencies will involve clarifying the relationship between embodied memory and apt function. In short, adaptation is a problem of semiotics: the organism must interpret the environment to fit well into it. This is well-illustrated by the constructed environments built by colonies of social insects, such as hives or nests, and the ancillary structures that contain them, forming an organism-like system known as a superorganism. The superorganism is marked by a kind of extended physiology, in that these constructed environments often serve as adaptive interfaces between the nest and ambient environment, and are constructed to manage the matter and energy flows between environments that constitute the process of adaptation. These constructed environments are also semiotic phenomena: interpretive structures, governed by information flow between the member insects and the structures they build. I review our findings on one such example: the mounds built by the fungus-cultivating termites of the genus Macrotermes. These structures are dynamic forms that are sustained by flows of soil from deep horizons up into the mound. The form, and hence the function, of the mound is determined by several environmental cues, most notably water and wind, as well as how termites interpret these cues, and signals that flow between termites, both directly and vicariously through the structures they build.

ASSOCIATIONS AND THEIR INFLUENCE ON THE VALUE-SENSE SELECTION OF STUDENTS

The article examines the association as a mechanism of manipulation of people (students) and how effective technique for self-discovery value-semantic selection of students, since associations are a projection of the inner world. Association have been widely used in psychoanalysis, Sigmund Freud (deep motivation, personal core "hell" mentality may reveal a unique method of psychological analysis – a method of "free" associations), Jung (reference to archetypes, causing people the same unconscious associations; archetype – hereditary memory storage, images and symbols laid down thousands of years). The article highlighted the factors affecting the value and meaning of human choice with the help of associations. The choice depends on the first impression and conditions, affect the integrity of the sensor or its individual elements, such as color, sound, smell, taste and touch. Generating meaning, the emergence of interest and the realization itself depends on the proposed context. The choice in different situations caused collective influence. Negatively impact on the process of meaning – the fear association, often in decision-making – the fear of loss.

Conservation of complex adaptability uniqueness in different Deschampsia antarctica Desv. plant genotypes under standardized growth condition in vitro

Uniqueness of complex adaptability index (united latent quality indicator of adaptability - ULQIA) has been shown to be taken place in plants having different chromosome number among Deschampsia antarctica Desv. (around Argentine Islands region, maritime Antarctic) cultivated under standardized growth condition in -vitro. ULQIA is assumed to express underlying in this plant adaptation process to uniqueness nature condition in dynamic hereditary memory special information in certain degree. It was shown that dynamic hereditary memory was saved in investigated plant genotypes under standardized growth condition in -vitro.

Darbishire expands his vision of heredity from Mendelian genetics to inherited memory

The British biologist A.D. Darbishire (1879–1915) responded to the rediscovery in 1900 of Mendel's theory of heredity by testing it experimentally, first in Oxford, then in Manchester and London. He summarised his conclusions in a textbook ‘Breeding and the Mendelian Discovery' (1911), in which he questioned whether Mendelism alone could explain all aspects of practical breeding experience. Already he had begun to think about an alternative theory to give greater emphasis to the widely held conviction among breeders regarding the inheritance of characteristics acquired during an individual's life. Redefining heredity in terms of a germ-plasm based biological memory, he used vocabulary drawn partly from sources outside conventional science, including the metaphysical/vitalistic writings of Samuel Butler and Henri Bergson. An evolving hereditary memory fitted well with the conception of breeding as a creative art aimed at greater economic efficiency. For evolution beyond human control he proposed a self-modifying process, claiming it to surpass in efficiency the chancy mechanism of natural selection proposed by Darwin. From his writings, including early chapters of an unfinished book entitled ‘An Introduction to a Biology’, we consider how he reached these concepts and how they relate to later advances in understanding the genome and the genetic programme.

‘His father’s voice’: Phonographs and Heredity in the Fiction of Samuel Butler

The article explores the interaction between concepts of heredity and technologies of voice recording and reproduction in the late-Victorian imagination through the example of Samuel Butler. Butler’s writing on evolutionary topics frequently conceptualized heredity as a record of ancestral voices echoing through their descendants. His Lamarckian view of evolution caused him to present heredity as analogous to the phonograph, recording the experiences of individuals, storing them in the germ plasm and reproducing them in the offspring. Theorists of hereditary memory such as Ewald Hering described it as a form of vibration and inscription, emphasizing its parallels with phonography. At the same time, language and the physical voice seemed equally haunted for Butler, resonating with the thoughts, feelings, and urges of past generations. I pursue these themes through a close reading of his posthumously published novel The Way of All Flesh (1903). Butler makes an interesting case study for this subject since his ideas about the inheritance of ancestral voices were inseparable from his complex personal relations with his family. His efforts to escape the influence of his parents were bound up with the notion of escaping the habitual ‘grooves’ in which they lived, thought, and spoke. Such escape sometimes seems impossible in Butler’s vision, with long-term heredity and immediate social convention rendering people echoes of their predecessors. However, the life experience of the individual offered possibilities for breaking with the voices of the past, etching new grooves of habit and redirecting old ones. Further, heredity in Butler’s vision was not a single, commanding voice but a cacophony of competing voices screaming to be heard. In this sense, what seemed like rebellion against the voice of one’s ancestor might turn out to be obedience towards another one. Butler conceived of intellectual influence in the same way, placing thinkers and writers in a pseudo-familial (and perhaps proto-Freudian) relationship with their predecessors. His concern with escaping ancestral voices existed in tension, though, with his desire to render his own voice immortal through his literary work.

A well posedness result for nonlinear viscoelastic equations with memory

We establish an existence, uniqueness and continuous dependence result for the weak solutions to the nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain |∂tu|ρ∂ttu−Δ∂ttu+γ(−Δ)θ∂tu−αΔu+∫0∞μ(s)Δu(t−s)ds+f(u)=h with Dirichlet boundary conditions. In particular, the parameter ρ belongs to the interval [0,4], the value 4 being critical for the Sobolev embeddings, while f can reach the critical polynomial order 5.

Exponential stability for a class of linear hyperbolic equations with hereditary memory

We establish a necessary and sufficient conditionof exponential stability for the contraction semigroup generatedby an abstract version of the linear differential equation$$∂_t u(t)-\int_0^\infty k(s)\Delta u(t-s)ds = 0$$modeling hereditary heat conduction of Gurtin-Pipkin type.